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8.0

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Topics: Radio Program, Elementary mathematics, Rooms

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8.0

audio

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Topics: Radio Program, BBC Radio, Member states of the United Nations, Former Spanish colonies, Island...

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4.0

audio

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Topics: Radio Program, Dairy products, Length, Great Britain, Celtic nations, Transport, Political...

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5.0

Jun 28, 2018
06/18

by
Matthew Ondrus; Emilie Wiesner

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This paper addresses the representation theory of the insertion-elimination Lie algebra, a Lie algebra that can be naturally realized in terms of tree-inserting and tree-eliminating operations on rooted trees. The insertion-elimination algebra admits a triangular decomposition in the sense of Moody and Pianzola, and thus it is natural to define a Whittaker module corresponding to a given algebra homomorphism. Among other results, we show that the standard Whittaker module is simple given...

Topics: Representation Theory, Mathematics

Source: http://arxiv.org/abs/1510.06998

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3.0

Jun 29, 2018
06/18

by
Nithin Govindarajan; Hassan Arbabi; Louis van Blargian; Timothy Matchen; Emma Tegling; Igor Mezić

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We apply an operator-theoretic viewpoint to a class of non-smooth dynamical systems that are exposed to event-triggered state resets. The considered benchmark problem is that of a pendulum which receives a downward kick under certain fixed angles. The pendulum is modeled as a hybrid automaton and is analyzed from both a geometric perspective and the formalism carried out by Koopman operator theory. A connection is drawn between these two interpretations of a dynamical system by means of...

Topics: Dynamical Systems, Mathematics

Source: http://arxiv.org/abs/1608.08734

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3.0

Jun 29, 2018
06/18

by
Shibashis Karmakar; SK. Monowar Hossein; Kallol Paul

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Let $\{f_n:n\in\mathbb{N}\}$ be a $J$-frame for a Krein space ${\textbf{\textit{K}}}$ and $P_M$ be a $J$-orthogonal projection from ${\textbf{\textit{K}}}$ onto a subspace $M$. In this article we find sufficient conditions under which $\{P_M(f_n):n\in\mathbb{N}\}$ is a $J$-frame for $P_M\textbf{\textit{K}}$ and $\{(I-P_M)f_n\}_{n\in{\mathbb{N}}}$ is a $J$-frame for $(I-P_M)\textbf{\textit{K}}$. We also introduce $J$-frame sequence for a Krein space ${\textbf{\textit{K}}}$ and study some...

Topics: Functional Analysis, Mathematics

Source: http://arxiv.org/abs/1609.08658

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3.0

Jun 30, 2018
06/18

by
Marko Budišić; Mihai Putinar

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If moments of singular measures are passed as inputs to the entropy maximization procedure, the optimization algorithm might not terminate. The framework developed in our previous paper demonstrated how input moments of measures, on a broad range of domains, can be conditioned to ensure convergence of the entropy maximization. Here we numerically illustrate the developed framework on simplest possible examples: measures with one-dimensional, bounded supports. Three examples of measures are used...

Topics: Complex Variables, Mathematics

Source: http://arxiv.org/abs/1411.0039

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8.0

Jun 30, 2018
06/18

by
Wuchen Li; Penghang Yin; Stanley Osher

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We propose a fast algorithm to approximate the optimal transport distance. The main idea is to add a Fisher information regularization into the dynamical setting of the problem, originated by Benamou and Brenier. The regularized problem is shown to be smooth and strictly convex, thus many classical fast algorithms are available. In this paper, we adopt Newton's method, which converges to the minimizer with a quadratic rate. Several numerical examples are provided.

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1704.04605

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5.0

Jun 30, 2018
06/18

by
Imdat Iscan; Erhan Set; M. Emin Ozdemir

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In this paper, the authors establish some new estimates for the remainder term of the midpoint, trapezoid, and Simpson formula using functions whose derivatives in absolute value at certain power are s-convex. Some applications to special means of real numbers are provided as well.

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1404.0905

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3.0

Jun 30, 2018
06/18

by
Gal Binyamini; Dmitry Novikov

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The \emph{Noetherian class} is a wide class of functions defined in terms of polynomial partial differential equations. It includes functions appearing naturally in various branches of mathematics (exponential, elliptic, modular, etc.). A conjecture by Khovanskii states that the \emph{local} geometry of sets defined using Noetherian equations admits effective estimates analogous to the effective \emph{global} bounds of algebraic geometry. We make a major step in the development of the theory of...

Topics: Complex Variables, Mathematics, Classical Analysis and ODEs, Algebraic Geometry

Source: http://arxiv.org/abs/1406.5959

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3.0

Jun 30, 2018
06/18

by
Chi-Kwong Li; Fuzhen Zhang

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We give a short proof of a recent result of Drury on the positivity of a $3\times 3$ matrix of the form $(\|R_i^*R_j\|_{\rm tr})_{1 \le i, j \le 3}$ for any rectangular complex (or real) matrices $R_1, R_2, R_3$ so that the multiplication $R_i^*R_j$ is compatible for all $i, j$, where $\|\cdot\|_{\rm tr}$ denotes the trace norm. We then give a complete analysis of the problem when the trace norm is replaced by other unitarily invariant norms.

Topics: Mathematics, Functional Analysis, Rings and Algebras

Source: http://arxiv.org/abs/1407.0331

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3.0

Jun 28, 2018
06/18

by
Eduard Feireisl; Antonin Novotny; Yongzhong Sun

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We consider a system of equations governing the motion of a viscous, compressible, and heat conducting liquid-like fluid, with a general EOS of Mie-Grueneisen type. In addition, we suppose that the viscosity coefficients may decay to zero for large values of the temperature. We show the existence of global-in-time weak solution, derive a relative energy inequality, and compare the weak solutions with strong one emanating from the same initial data - the weak strong uniqueness property.

Topics: Analysis of PDEs, Mathematics

Source: http://arxiv.org/abs/1510.07578

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3.0

Jun 28, 2018
06/18

by
Vilmos Komornik; Anna Chiara Lai; Paola Loreti

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A classical theorem of Ingham extended Parseval's formula of the trigonometrical system to arbitrary families of exponentials satisfying a uniform gap condition. Later his result was extended to several dimensions, but the optimal integration domains have only been determined in very few cases. The purpose of this paper is to determine the optimal connected integration domains for all regular two-dimensional lattices.

Topics: Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1512.04212

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7.0

Jun 29, 2018
06/18

by
Naoki Imai; Yoichi Mieda

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In this paper, we give a notion of the potentially good reduction locus of a Shimura variety. It consists of the points which should be related with motives having potentially good reductions in some sense. We show the existence of such locus for a Shimura variety of preabelian type. Further, we construct a partition of the adic space associated to a Shimura variety of preabelian type, which is expected to describe degenerations of motives. Using this partition, we prove that the cohomology of...

Topics: Number Theory, Algebraic Geometry, Mathematics

Source: http://arxiv.org/abs/1611.04839

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Speaker: Oleg Musin Date: November, 2003

Topics: Mathematics, lectures

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5.0

Jun 30, 2018
06/18

by
Robert McRae

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We revisit the construction of integral forms for vertex (operator) algebras $V_L$ based on even lattices $L$ using generators instead of bases, and we construct integral forms for $V_L$-modules. We construct integral forms for vertex (operator) algebras based on highest-weight modules for affine Lie algebras and we exhibit natural generating sets. For vertex operator algebras in general, we give conditions showing when an integral form contains the standard conformal vector generating the...

Topics: Quantum Algebra, Mathematics, Representation Theory

Source: http://arxiv.org/abs/1401.2505

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4.0

Jun 30, 2018
06/18

by
Y. S. Kim; A. K. Rathie; R. B. Paris

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The aim in this note is to provide a generalization of an interesting entry in Ramanujan's Notebooks that relate sums involving the derivatives of a function Phi(t) evaluated at 0 and 1. The generalization obtained is derived with the help of expressions for the sum of terminating 3F2 hypergeometric functions of argument equal to 2, recently obtained in Kim et al. [Two results for the terminating 3F2(2) with applications, Bull. Korean Math. Soc. 49 (2012) pp. 621{633]. Several special cases are...

Topics: Complex Variables, Mathematics

Source: http://arxiv.org/abs/1401.3636

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4.0

Jun 30, 2018
06/18

by
Vladimir Blinovsky

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We find the formula for the maximal cardinality of the family of $n$-tuples from ${[n]\choose k}$ with does not have $\ell$--matching. This formula after some analytical issues can be reduce to the Erd\"os's Matching formula. Also we prove the conjecture about the cardinality of maximal $s$-wise $t$-intersecting family of $k$-element subsets of $[n]$. In the proofs we use original method which we have already used in the proof of Mikl\'os-Manikam-Singhi conjecture in \cite{1}. We call this...

Topics: Mathematics, Combinatorics

Source: http://arxiv.org/abs/1402.1505

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Jun 27, 2018
06/18

by
B. Ravinder

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Let $\mathfrak{g}$ be a finite-dimensional complex simple Lie algebra with highest root $\theta$ and let $\mathfrak{g}[t]$ be the corresponding current algebra. In this paper, we consider the $\mathfrak{g}[t]$-stable Demazure modules associated to integrable highest weight representations of the affine Lie algebra $\widehat{\mathfrak{g}}$. We prove that the fusion product of Demazure modules of a given level with a single Demazure module of a different level and with highest weight a multiple...

Topics: Representation Theory, Mathematics, Quantum Algebra

Source: http://arxiv.org/abs/1504.01537

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Jun 26, 2018
06/18

by
Charles Frohman; Joanna Kania-Bartoszynska

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A version of Dehn's algorithm for simple diagrams on a once punctured surface representing simple diagrams on a closed surface is presented

Topics: Mathematics, Geometric Topology

Source: http://arxiv.org/abs/1502.03503

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7.0

Jun 26, 2018
06/18

by
Mancho Manev

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The object of study are almost complex manifolds with a pair of Norden metrics, mutually associated by means of the almost complex structure. More precisely, a torsion-free connection and tensors with geometric interpretation are found which are invariant under the twin interchange, i.e. the swap of the counterparts of the pair of Norden metrics and the corresponding Levi-Civita connections. A Lie group depending on four real parameters is considered as an example of a 4-dimensional manifold of...

Topics: Mathematics, Differential Geometry

Source: http://arxiv.org/abs/1502.06779

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3.0

Jun 30, 2018
06/18

by
G. C. Bento; A. Soubeyran

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The "Habitual domain" (HD) approach and the "Variational rationality" (VR) approach belong to the same strongly interdisciplinary and very dispersed area of research: human stability and change dynamics (see Soubeyran, 2009, 2010, for an extended survey), including physiological, physical, psychological and strategic aspects, in Psychology, Economics, Management Sciences, Decision theory, Game theory, Sociology, Philosophy, Artificial Intelligence,.... These two approaches...

Topics: Mathematics, Optimization and Control

Source: http://arxiv.org/abs/1403.7032

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4.0

Jun 30, 2018
06/18

by
Gábor Székelyhidi

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This paper is a survey of some recent progress on the study of Calabi's extremal K\"ahler metrics. We first discuss the Yau-Tian-Donaldson conjecture relating the existence of extremal metrics to an algebro-geometric stability notion and we give some example settings where this conjecture has been established. We then turn to the question of what one expects when no extremal metric exists.

Topics: Mathematics, Differential Geometry

Source: http://arxiv.org/abs/1405.4836

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6.0

Jun 30, 2018
06/18

by
Andrew R. Francis; Milan Stehlik; Henry P. Wynn

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Confidence nets, that is, collections of confidence intervals that fill out the parameter space and whose exact parameter coverage can be computed, are familiar in nonparametric statistics. Here, the distributional assumptions are based on invariance under the action of a finite reflection group. Exact confidence nets are exhibited for a single parameter, based on the root system of the group. The main result is a formula for the generating function of the coverage interval probabilities. The...

Topics: Mathematics, Statistics Theory, Statistics, Group Theory

Source: http://arxiv.org/abs/1407.8375

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Jun 30, 2018
06/18

by
Darij Grinberg; Victor Reiner

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These notes -- originating from a one-semester class by their second author at the University of Minnesota -- survey some of the most important Hopf algebras appearing in combinatorics. After introducing coalgebras, bialgebras and Hopf algebras in general, we study the Hopf algebra of symmetric functions, including Zelevinsky's axiomatic characterization of it as a "positive self-adjoint Hopf algebra" and its application to the representation theory of symmetric and (briefly) finite...

Topics: Mathematics, Rings and Algebras, Combinatorics

Source: http://arxiv.org/abs/1409.8356

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7.0

Jun 28, 2018
06/18

by
Giuseppe Floridia

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In this paper we obtain well-posedness for a class of semilinear weakly degenerate reaction-diffusion systems with Robin boundary conditions. This result is obtained through a Gagliardo-Nirenberg interpolation inequality and some embedding results for weighted Sobolev spaces.

Topics: Functional Analysis, Optimization and Control, Analysis of PDEs, Mathematics

Source: http://arxiv.org/abs/1509.05510

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4.0

Jun 28, 2018
06/18

by
Dmitrii Zhelezov

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We prove that if $B$ is a set of $N$ positive integers such that $B\cdot B$ contains an arithmetic progression of length $M$, then for some absolute $C > 0$, $$ \pi(M) + C \frac {M^{2/3}}{\log^2 M} \leq N, $$ where $\pi$ is the prime counting function. This improves on previously known bounds of the form $N = \Omega(\pi(M))$ and gives a bound which is sharp up to the second order term, as Pach and S\'andor gave an example for which $$ N < \pi(M)+ O\left(\frac {M^{2/3}}{\log^2 M} \right)....

Topics: Number Theory, Mathematics

Source: http://arxiv.org/abs/1510.05411

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5.0

Jun 28, 2018
06/18

by
Junping Li; Juan Wang; Yanchao Zang

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In this paper, we consider $n$-type Markov branching processes with immigration and resurrection. The uniqueness criteria are first established. Then, a new method is found and the explicit expression of extinction probability is successfully obtained in the absorption case, the mean extinction time is also given. The recurrence and ergodicity criteria are given if the state ${\bf 0}$ is not absorptive. Finally, if the resurrection rates are same as the immigration rates, the branching property...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1512.04696

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6.0

Jun 29, 2018
06/18

by
Whitney George; Janine E. Janoski

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Consider a $n \times n$ tic-tac-toe board. In each field of the board, draw a smaller $n\times n$ tic-tac-toe board. Now let super tic-tac-toe (STTT) be a game where each player's move dictates which field on the larger board a player must make their next move. We will play an impartial game of STTT where each player uses X. We define a set of actions on a game board which gives rise to a group-action on the game that creates equivalent games. We will discuss how the structure of this...

Topics: Combinatorics, Mathematics

Source: http://arxiv.org/abs/1606.04779

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3.0

Jun 30, 2018
06/18

by
Alexios Balatsoukas-Stimming; Andrew Charles Mallory Austin; Pavle Belanovic; Andreas Burg

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Hardware imperfections can significantly reduce the performance of full-duplex wireless systems by introducing non-idealities and random effects that make it challenging to fully suppress self-interference. Previous research has mostly focused on analyzing the impact of hardware imperfections on full-duplex systems, based on simulations and theoretical models. In this paper, we follow a measurement-based approach to experimentally identify and isolate these hardware imperfections leading to...

Topics: Mathematics, Computing Research Repository, Information Theory

Source: http://arxiv.org/abs/1412.4542

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3.0

Jun 29, 2018
06/18

by
Richard Evan Schwartz

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Let R_s(r)=sign(s)/r^s be the Riesz s-energy potential. (This is the usual power-law potential.) This monograph proves the existence of a computable number S=15.048... such that the triangular bi-pyramid is the unique minimizer with respect to R_s, amongst all 5-point configurations on the sphere, if and only if s lies in (-2,0) or (0,S). This establishes the existence of the long-conjectured phase transition constant in 5-point energy minimization.

Topics: Optimization and Control, Mathematics

Source: http://arxiv.org/abs/1610.03303

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5.0

Jun 30, 2018
06/18

by
Prajakta Nimbhorkar; Arvind Rameshwar

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We consider the problem of matching applicants to posts where applicants have preferences over posts. Thus the input to our problem is a bipartite graph G = (A U P,E), where A denotes a set of applicants, P is a set of posts, and there are ranks on edges which denote the preferences of applicants over posts. A matching M in G is called rank-maximal if it matches the maximum number of applicants to their rank 1 posts, subject to this the maximum number of applicants to their rank 2 posts, and so...

Topics: Data Structures and Algorithms, Computing Research Repository, Discrete Mathematics

Source: http://arxiv.org/abs/1704.00899

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3.0

Jun 30, 2018
06/18

by
Guido Montufar; Johannes Rauh; Nihat Ay

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We consider three different approaches to define natural Riemannian metrics on polytopes of stochastic matrices. First, we define a natural class of stochastic maps between these polytopes and give a metric characterization of Chentsov type in terms of invariance with respect to these maps. Second, we consider the Fisher metric defined on arbitrary polytopes through their embeddings as exponential families in the probability simplex. We show that these metrics can also be characterized by an...

Topics: Mathematics, Statistics Theory, Differential Geometry, Statistics

Source: http://arxiv.org/abs/1404.0198

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4.0

Jun 30, 2018
06/18

by
Biagio Ricceri

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In this paper, we establish some results about the singular points of certain non-monotone potential operators. Here is a sample: If $X$ is an infinite-dimensional reflexive real Banach space and if $T:X\to X^*$ is a non-monotone, closed, continuous potential operator such that the functional $x\to \int_0^1T(sx)(x)ds$ is sequentially weakly lower semicontinuous and $\lim_{\|x\|\to +\infty}(\int_0^1T(sx)(x)ds+\varphi(x))=+\infty$ for all $\varphi\in X^*$, then the set of all singular points of...

Topics: Functional Analysis, Mathematics

Source: http://arxiv.org/abs/1406.1026

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7.0

Jun 30, 2018
06/18

by
Abhay Ashtekar

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In asymptotically Minkowski space-times, one finds a surprisingly rich interplay between geometry and physics in both the classical and quantum regimes. On the mathematical side it involves null geometry, infinite dimensional groups, symplectic geometry on the space of gravitational connections and geometric quantization via K\"ahler structures. On the physical side, null infinity provides a natural home to study gravitational radiation and its structure leads to several interesting...

Topics: High Energy Physics - Theory, Mathematics, Mathematical Physics, General Relativity and Quantum...

Source: http://arxiv.org/abs/1409.1800

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3.0

Jun 30, 2018
06/18

by
Silvia Lassalle; Eve Oja; Pablo Turco

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Fixed a Banach operator ideal $\mathcal A$, we introduce and investigate two new approximation properties, which are strictly weaker than the bounded approximation property (BAP) for $\mathcal A$ of Lima, Lima and Oja (2010). We call them the weak BAP for $\mathcal A$ and the local BAP for $\mathcal A$, showing that the latter is in turn strictly weaker than the former. Under this framework, we address the question of approximation properties passing from dual spaces to underlying spaces. We...

Topics: Functional Analysis, Mathematics

Source: http://arxiv.org/abs/1410.5670

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5.0

Jun 29, 2018
06/18

by
Javier Roa; Hodei Urrutxua; Jesús Peláez

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The need for the extra dimension in Kustaanheimo-Stiefel (KS) regularization is explained by the topology of the Hopf fibration, which defines the geometry and structure of KS space. A trajectory in Cartesian space is represented by a four-dimensional manifold, called the fundamental manifold. Based on geometric and topological aspects classical concepts of stability are translated to KS language. The separation between manifolds of solutions generalizes the concept of Lyapunov stability. The...

Topics: Space Physics, Solar and Stellar Astrophysics, Physics, Mathematics, Astrophysics, Mathematical...

Source: http://arxiv.org/abs/1604.06673

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5.0

Jun 30, 2018
06/18

by
Lukáš Malý

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Density of Lipschitz functions in Newtonian spaces based on quasi-Banach function lattices is discussed. Newtonian spaces are first-order Sobolev-type spaces on abstract metric measure spaces defined via (weak) upper gradients. Our main focus lies on metric spaces with a doubling measure that support a $p$-Poincar\'e inequality. Absolute continuity of the function lattice quasi-norm is shown to be crucial for approximability by (locally) Lipschitz functions. The proof of the density result...

Topics: Functional Analysis, Mathematics

Source: http://arxiv.org/abs/1404.7068

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5.0

Jun 30, 2018
06/18

by
Paul Honeine

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Many signal processing and machine learning methods share essentially the same linear-in-the-parameter model, with as many parameters as available samples as in kernel-based machines. Sparse approximation is essential in many disciplines, with new challenges emerging in online learning with kernels. To this end, several sparsity measures have been proposed in the literature to quantify sparse dictionaries and constructing relevant ones, the most prolific ones being the distance, the...

Topics: Statistics, Mathematics, Computing Research Repository, Information Theory, Computer Vision and...

Source: http://arxiv.org/abs/1409.6045

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5.0

Jun 30, 2018
06/18

by
Ralph Chill; Sebastian Krol

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We prove weighted estimates for singular integral operators which operate on function spaces on a half-line. The class of admissible weights includes Muckenhoupt weights and weights satisfying Sawyer's one-sided conditions. The kernels of the operators satisfy relaxed Dini conditions. We apply the weighted estimates to extrapolation of maximal $L^p$ regularity of first order, second order and fractional order Cauchy problems into weighted rearrangement invariant Banach function spaces. In...

Topics: Mathematics, Functional Analysis, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1410.3457

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Jun 30, 2018
06/18

by
Boris Botvinnik; Johannes Ebert; Oscar Randal-Williams

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We study the homotopy type of the space of metrics of positive scalar curvature on high-dimensional compact spin manifolds. Hitchin used the fact that there are no harmonic spinors on a manifold with positive scalar curvature to construct a secondary index map from the space of positive scalar metrics to a suitable space from the real $K$-theory spectrum. Our main results concern the nontriviality of this map. We prove that for $2n \geq 6$, the natural $KO$-orientation from the infinite loop...

Topics: Mathematics, Algebraic Topology, Differential Geometry, Geometric Topology

Source: http://arxiv.org/abs/1411.7408

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4.0

Jun 29, 2018
06/18

by
Nikolaj Glazunov

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This article consisted of an elementary introduction to deformation theory of varieties, schemes and manifolds, with some applications to local and global shtukas and fever to Newton polygons of $p$-divisible groups . Soft problems and results mainly are considered. In the framework we give review of some novel results in the theory of local shtukas, Anderson-modules, global shtukas, Newton polygons of $p$-divisible groups and on deformations of $p$-divisible groups with given Newton polygons.

Topics: Number Theory, Mathematical Physics, Mathematics

Source: http://arxiv.org/abs/1601.01991

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5.0

Jun 29, 2018
06/18

by
V. V Mykhaylyuk

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It is investigated the existence of a separately continuous function $f:X\times Y\to \mathbb R$ with an onepoint set of discontinuity for topological spaces $X$ and $Y$ which satisfy compactness type conditions. In particular, it is shown that for compact spaces $X$ and $Y$ and nonizolated points $x_0\in X$ and $y_0\in Y$ there exists a separately continuous function $f:X\times Y\to \mathbb R$ with the set $\{(x_0,y_0)\}$ of discontinuity points if and only if there exist sequences of nonempty...

Topics: General Topology, Mathematics

Source: http://arxiv.org/abs/1601.02744

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3.0

Jun 30, 2018
06/18

by
José F. Cariñena; Fernando Falceto; Janusz Grabowski; Manuel F. Rañada

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After a short review of the classical Lie theorem, a finite dimensional Lie algebra of vector fields is considered and the most general conditions under which the integral curves of one of the fields can be obtained by quadratures in a prescribed way will be discussed, determining also the number of quadratures needed to integrate the system. The theory will be illustrated with examples andbn an extension of the theorem where the Lie algebras are replaced by some distributions will also be...

Topics: Classical Analysis and ODEs, Mathematical Physics, Nonlinear Sciences, Exactly Solvable and...

Source: http://arxiv.org/abs/1701.03907

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3.0

Jun 30, 2018
06/18

by
Michael Anshelevich; Matthew Gaikema; Madeline Hansalik; Songyu He; Nathan Mehlhop

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We compute the number of ways a given permutation can be written as a product of exactly $k$ transpositions. We express this number as a linear combination of explicit geometric sequences, with coefficients which can be computed in many particular cases. Along the way we prove several symmetry properties for matrices associated with bipartite graphs, as well as some general (likely known) properties of Young diagrams. The methods involve linear algebra, enumeration of border strip tableau, and...

Topics: Combinatorics, Mathematics

Source: http://arxiv.org/abs/1702.06093

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7.0

Jun 29, 2018
06/18

by
Michael B. Cohen

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The recent work by Marcus, Spielman and Srivastava proves the existence of bipartite Ramanujan (multi)graphs of all degrees and all sizes. However, that paper did not provide a polynomial time algorithm to actually compute such graphs. Here, we provide a polynomial time algorithm to compute certain expected characteristic polynomials related to this construction. This leads to a deterministic polynomial time algorithm to compute bipartite Ramanujan (multi)graphs of all degrees and all sizes.

Topics: Combinatorics, Data Structures and Algorithms, Computing Research Repository, Mathematics

Source: http://arxiv.org/abs/1604.03544

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3.0

Jun 29, 2018
06/18

by
Ahmad Sabihi

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We approach a new proof of the strong Goldbach's conjecture for sufficiently large even integers by applying the Dirichlet's series. Using the Perron formula and the Residue Theorem in complex variable integration, one could show that any large even integer is demonstrated as a sum of two primes. In this paper,the Riemann Hypothesis is assumed to be true in throughout the paper. A novel function is defined on the natural numbers set.This function is a typical sieve function.Then based on this...

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1605.08938

Topics: mathematics, geometry

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7.0

Jun 30, 2018
06/18

by
Eric Cancès; Nahia Mourad

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In this article, we consider the extended Kohn-Sham model for atoms subjected to cylindrically-symmetric external potentials. The variational approximation of the model and the construction of appropriate discretization spaces are detailed together with the algorithm to solve the discretized Kohn-Sham equations used in our code. Using this code, we compute the occupied and unoccupied energy levels of all the atoms of the first four rows of the periodic table for the reduced Hartree-Fock (rHF)...

Topics: Mathematical Physics, Mathematics

Source: http://arxiv.org/abs/1702.01004

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3.0

Jun 30, 2018
06/18

by
Nicholas D. Alikakos; Giorgio Fusco

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We extend the Caffarelli-Cordoba estimates to the vector case in two ways, one of which has no scalar counterpart, and we give a few applications for minimal solutions.

Topics: Mathematics, Analysis of PDEs, Differential Geometry

Source: http://arxiv.org/abs/1403.7608